It is known that in order to reconstruct a signal by performing digital sampling, the sampling rate (the so-called Nyquist frequency) should be at least twice the maximum frequency component of the signal of interest (Nyquist sampling theorem). However, electrical circuits generate and can pick up noise. Noise is undesirable and can contain signal components with frequency higher than the maximum frequency component of the signal of interest. These components may then alias into the frequency range of the signal of interest and thus lead to erroneous sampling results.
To ensure that the frequency range of the signal of interest is limited, a filtered sampling circuit, i.e. a low pass filter that passes low frequency components but attenuates the high frequency components, is added during sampling the signal. This low pass filter prevents the high frequency components from being sampled by attenuating signal components with frequency higher than the Nyquist frequency.
Filtered sampling circuits are commonly used to sample the signal at a predetermined sampling rate and at the same time to filter the sampled signal with a predetermined cut off frequency. The cut-off frequency of the filtered sampling circuit depends on the sampling rate, an observation time, i.e. the time during which the input signal is fed continuously to the filtered sampling circuit and a time constant of the filtered sampling circuit.
At low sampling rates (low operational frequency), the filtered sampling circuits need to work with a very large time constant. The input signal needs to be held, e.g. by a large capacitor, for a relatively long observation time. The large capacitor holding the charge can leak and lead to overall inaccuracy in the digital sampling process.